1 Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104, National Bureau of Economic Research, and Centre for Economic Policy Research. · 2 Department of Economics, Duke University, P.O. Box 90097, Durham, NC 27008, and Federal Reserve Bank of Atlanta. · 3 Department of Economics, New York University, 269 Mercer Street, New York, NY 10003, and Hoover Institution. · 4 Department of Economics and Woodrow Wilson School, Princeton University, 321 Bendheim Hall, Princeton, NJ 08544.
Abstract
The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A, B, C, D) that define a state space system for a vector of observables. An associated state space system (A, ^ B,C, ^D) determines a vector autoregression for those same observables. We present a simple condition for checking when these two state space systems match up and when they do not when there are equal numbers of economic and VAR shocks. We illustrate our condition with a permanent income example.